Theorie-Palaver

Reduced hadronic uncertainty in V_{ud} and first-row CKM unitarity.

Mikhail Gorshteyn, Institut fr Kernphysik, JGU, Mainz, Germany

Radiative corrections to neutron beta-decay have been fundamental for establishing the
electroweak model. Universality of the weak interaction and conservation of vector current lead to the
requirement of unitarity of the CKM mixing matrix. Unitarity in the first row, |V_{ud}|^2+|V_{us}|^2+|V_{ub}|^2=1
belongs to the most stringent tests of the Standard Model and beyond. Current PDG value is in good
agreement with unitarity, |V_{ud}|^2+|V_{us}|^2+|V_{ub}|^2=0.9994 +- 0.0005, and the central value
and the uncertainty are dominated by those due to the upper-left corner element |V_{ud}|=0.97420(10)_{exp}(18)_{th},
which is obtained from analysis of superallowed nuclear decays. The uncertainty of V_{ud} is dominated
by the theoretical uncertainty related to the gamma-W-box diagram which depends on hadronic and
nuclear structure. The hadronic part has been addressed by Marciano and Sirlin, while the nuclear part
by Towner and Hardy. To test previous analyses, we applied dispersion relations to the calculation of the
gamma-W-box correction, and used data on neutrino and antineutrino scattering to better constrain
the input in the dispersion integral. We were able to reduce the hadronic uncertainty by almost a factor 2,
|V_{ud}|=0.97366(10)_{exp}(11)_{th}. However, the central value shifted considerably, raising tension
with unitarity, |V_{ud}|^2+|V_{us}|^2+|V_{ub}|^2=0.9984 +- 0.0004. Ongoing work is concentrated on
proposing new measurements with polarized electrons and neutrinos to test our new analysis in a more
direct and model-independent way, and on reevaluating the nuclear structure corrections within the
dispersive framework.